No abstract

A simple unifying view of the exceptional Lie algebras is presented. The underlying Jordan pair content and role are exhibited. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external su(3) symmetry. Eventual physical applications and implications of the theory are outlined.

No abstract

Abstract. We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions of the noise's correlation time and strength the fluctuations in the driving field cancel out. In this way, we provide theoretical support for previous numerical simulations. We also briefly comment on the error due to the mismatch between the real and the nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.